Tim answered all the questions on his math test but got $10$ answers wrong. He received $4$ points for every correct answer, and there was no penalty for wrong answers. His score was $76$ points. Write an equation to determine the total number of questions $(q)$ on Tim's math test. Find the total number of questions on his math test.
Explanation: Let $q$ be the total number of questions on Tim's math test. Tim answered correctly on $q-10$ of the math problems. Each correct answer was worth $4$ points. His total score was $4(q-10)$. Since his test score was $76$ points, let's set this equal to $76$ : $ 4(q-10)=76$ Now, let's solve the equation to find the total number of questions $(q)$ on Tim's math test. $\begin{aligned}4(q-10)&=76\\&\\ \dfrac{4(q-10)}{{4}}&=\dfrac{76}{{4}}&&\text{divide both sides by ${4}$}\\ \\ q-10&=19\\ \\ q-{10}{+10}&=19{+10}&&{\text{add }} {10} \text{ to both sides}\\ \\ q&=29\end{aligned}$ The equation is $4(q-10)=76$. The total number of questions on Tim's math test was $29$.